|5-i/1+i| eching

$$| \frac { 5 - i } { 1 + i } |$$

Baholash

$$\sqrt{13}\approx 3,605551275$$

Yechim qadamlari

\frac{5-i}{1+i}ning surat va maxrajini murakkab tutash maxraj 1-i bilan ko‘paytiring.

$$|\frac{\left(5-i\right)\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}|$$

Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$|\frac{\left(5-i\right)\left(1-i\right)}{1^{2}-i^{2}}|$$

Ta’rifi bo‘yicha, i^{2} – bu -1. Maxrajini hisoblang.

$$|\frac{\left(5-i\right)\left(1-i\right)}{2}|$$

Binomlarni ko‘paytirgandek 5-i va 1-i murakkab sonlarni ko‘paytiring.

$$|\frac{5\times 1+5\left(-i\right)-i-\left(-i^{2}\right)}{2}|$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$|\frac{5\times 1+5\left(-i\right)-i-\left(-\left(-1\right)\right)}{2}|$$

5\times 1+5\left(-i\right)-i-\left(-\left(-1\right)\right) ichidagi ko‘paytirishlarni bajaring.

$$|\frac{5-5i-i-1}{2}|$$

5-5i-i-1 ichida real va mavhum qismlarni birlashtiring.

$$|\frac{5-1+\left(-5-1\right)i}{2}|$$

5-1+\left(-5-1\right)i ichida qo‘shishlarni bajaring.

$$|\frac{4-6i}{2}|$$

2-3i ni olish uchun 4-6i ni 2 ga bo‘ling.

$$|2-3i|$$

a+bi murakkab soning moduli – \sqrt{a^{2}+b^{2}}. 2-3i moduli – \sqrt{13}.

$$\sqrt{13}$$

Ashyoviy qism

$$\sqrt{13} = 3,605551275$$